Let in even-dimensional a±nely connected space without a
torsion A2m be given a composition Xm£Xm by the affinor a¯
®. The affinor b¯
®,
determined with the help of the eigen-vectors of the matrix (a¯
®), de¯nes the
second composition Ym £ Y m. Conjugate compositions are introduced by the
condition: the a±nors of any of both compositions transform the vectors from
the one position of the composition, generated by the other a±nor, in the
vectors from the another its position. It is proved that the compositions de¯ne
by a±nors a¯
® and b¯
® are conjugate. It is proved also that if the composition
Xm£Xm is Cartesian and composition Ym£Y m is Cartesian or chebyshevian,
or geodesic than the space A2m is affine.